cvxopt

CVXOPT is an open-source Python package for convex optimization that provides a set of solvers and modeling tools for building and solving convex programs. It offers interfaces to standard convex problem formulations and is designed to work with NumPy, SciPy, and other numerical libraries. The package provides its own matrix type, cvxopt.matrix, and can interoperate with NumPy arrays via conversion utilities.

The library supports several classes of convex optimization problems, including quadratic programming (QP), linear programming (LP), second-order cone programming (SOCP), and semidefinite programming (SDP). Solvers implement interior-point methods and accept problems in standard forms such as minimize 1/2 x^T P x + q^T x subject to Gx ≤ h and Ax = b.

CVXOPT is implemented primarily in C with Python bindings and relies on optimized linear algebra libraries (BLAS/LAPACK) for performance. The Python interface is accessed through modules such as cvxopt.solvers and cvxopt.blas, with functions like qp, lp, socp, and sdp to solve respective problems. Results typically include the optimal solution, objective value, and solver status.

Installation is via standard Python packaging tools (for example, pip install cvxopt), with binary wheels available for common platforms. The project is released under an open-source license.

Applications include finance, engineering, control, and machine learning research, where convex optimization problems arise. While powerful and versatile, CVXOPT may be slower or less convenient for very large-scale problems compared with specialized commercial solvers, and some users opt to use higher-level interfaces such as CVXPY on top of CVXOPT backends.